Answer:
The game will lose by 1.94 points .
Solution:
A player who rolls a 3, 4, 10, 11, or 12 wins 5 points and player who rolls a 5, 6, 7, 8, or 9 loses 5 points.
As two dice are rolled hence the total chances are [tex](6\times6) = 36[/tex].
The chances of 3 in rolling are (1,2), (2,1)
So the probability of rolling 3 is [tex]\frac{2}{36}[/tex]
The chance of 4 in rolling are (1,3),(3,1), (2,2)
So the probability of rolling 4 is [tex]\frac{3}{36}[/tex]
The chance of 10 in rolling are (5,5),(4,6), (6,4)
So the probability of rolling 10 is [tex]\frac{3}{36}[/tex]
The chance of 11 in rolling are (5,6),(6,5)
So the probability of rolling 11 is [tex]\frac{2}{36}[/tex]
The chance of 12 in rolling are (6,6)
So the probability of rolling 12 is [tex]\frac{1}{36}[/tex]
So the total probability of winning is [tex]\left(\frac{2}{36}+\frac{3}{36}+\frac{3}{36}+\frac{2}{36}+\frac{1}{36}\right)=\frac{11}{36}[/tex]
Hence the probability of losing is [tex]\left(1-\frac{11}{36}\right)=\frac{25}{36}[/tex]
So the expected value of the game [tex]=\left(\frac{11}{36}\right) \times 5+\left(\frac{25}{36}\right) \times(-5)=\left(\frac{55}{36}-\frac{125}{36}\right)=\left(-\frac{70}{36}\right)=-1.94[/tex]
Therefore, the game will lose by 1.94 points
player will "WIN" "5" points by rolling a 2.
Just took the test on Edmentum this is correct.
